Building the ultimate Solar System part 4: two ninja moves — moons and co-orbital planets
We are building the ultimate Solar System. In Part 1 we chose the right star. In Part 2 we chose the right planets. In Part 3 we chose the right orbits for the planets.
Today’s job: Discovering two ninja moves that will allow us to pack way more worlds in the habitable zone.
The last post (part 3: choosing the right orbits) was pretty simple stuff. You can cram more small planets into the habitable zone than big ones. Nothing too shocking. Well, learning the basics always comes before the ninja moves.
What makes these moves ninja (to use ninja as an adjective) is that they put more than one world on the same orbit. This means that we can pack a lot more worlds into our star’s habitable zone. It’s like the 6-pack: a way to cram more awesomeness into a limited space.
Let’s meet the ninjas.
NINJA MOVE 1: MOONS. A planet’s moons orbit the star just like the planet does. I used this to my advantage this when I built a better Solar System.
Here are the large moons in the Solar System:
The biggest Solar System moons orbit the biggest planets (Jupiter and Saturn). Systems of moons form like mini-Solar Systems, in disks of gas and dust around gas giant planets. [In fact, large Solar System moons have some properties in common with extra-solar planets]. The moons are located very close to the gas giants. The orbits of the most distant large moons are only about 30 times larger than the radius of their host planet. In comparison, Earth’s orbit is about 200 times larger than the radius of the Sun.
We want worlds in our ultimate Solar System that are a little bigger than these large moons. We want worlds about half to twice Earth’s size. Although there is some debate, I’m going to allow any gas giant that is Saturn-sized or larger to have large moons.
In the Solar System, Jupiter has the most (four). Given how close-in the Solar System moons are located, large moons are likely to stay close. But how many big moons could a gas giant have? Well, at least as many as Jupiter (four). But probably not that many more. The orbits of planets and moons tend to be spaced logarithmically. Think, 1, 10, 100, 1000 rather than 10, 20, 30, 40. The farther from the star/planet, the bigger the spaces between planets/moons. If the zone with large moons extends from 5 to 50 times the planet’s radius, this only gives us room for 5 large moons spaced like Jupiter’s. We’ll stick with a maximum of 5 large moons per gas giant planet.
Could a planet like Earth have a moon large enough for life? The jury is still out on how to form such a moon (probably by a giant impact between two big growing planets). But there is no reason not to consider this possibility. However, an Earth-sized planet probably could not have more than one large moon remain stable. [Note that Earth may have had a second large moon that crashed into the Moon!] In fact, if an Earth-sized planet had an Earth-sized moon, this would essentially be a binary planet. Each planet would orbit the other, as the pair orbited the star. Pretty awesome concept! Pluto and Charon are basically a binary (minor) planet. Charon is about half as big as Pluto and about 10% as massive.
A binary Earth would behave mostly like the Earth-Moon system does today. But tides would be much stronger. The two Earths always show each other the same face as their orbit their common center of gravity.
The planets each make one full rotation for each orbit around each other. This means that a day should be about a month in length. This may have some impact on the planets’ climate, but probably in a good way. Slowly-rotating planets may remain habitable closer to their stars than fast-rotating planets.
SUMMARY: A gas giant could have up to 5 moons large enough to be habitable. Planets in our chosen size range can also have large moons but probably only one.
NINJA MOVE 2: CO-ORBITAL PLANETS. When you hear the word “Trojan”, you probably don’t think of asteroids. But they are real! What is interesting about the Trojan asteroids is that they share the same orbit as Jupiter. And so do the “Greek” asteroids. This image shows where these asteroids are located.
The Trojan and Greek asteroids are about 60 degrees in front of and behind Jupiter. Normally, when an asteroid comes close to Jupiter, the planet’s strong gravity deflects the asteroid. Eventually the asteroid’s orbit takes it close to Jupiter. Jupiter launches the asteroid out of the Solar System.
The Trojan and Greek asteroids live on islands of stability. It turns out that the positions 60 degrees ahead and behind Jupiter are protected from its strong gravity. These are called the L4 and L5 points (the L is for Lagrange, who discovered that they are stable). Since they share the same orbit, they are also called co-orbitals.
Asteroids that orbit at L4 or L5 are stable. They can orbit happily at those points forever. They don’t stay exactly at L4 or L5; rather, they trace little circles about those points. That is why the Trojans and Greeks are clouds instead of all being found at a single point.
Co-orbital (aka Trojan) planets are like a person walking with a man-eating tiger but always staying behind it, just in its blind spot. Perfectly safe, it turns out, but with mortal (gravitational) danger right nearby.
L4 or L5 would be stable islands for an Earth-sized planet. Even one with a large moon. In fact, two Earth-sized planets — one at L4 and one at L5 — could be stable. In some circumstances L4 or L5 could even be stable for another gas giant (but just one).
Now switch out Jupiter for Earth. Earth also has L4 and L5 points. Earth even has a Trojan asteroid. Two Earth-sized planets can share an orbit in their mutual L4/L5 points. Separated by 60 degrees, the two planets’ orbits are stable.
Systems of planets that include co-orbitals have to be a bit more widely-spaced. Otherwise they become unstable. That means that we can’t cram quite as many orbits into the habitable zone.
Even though there are fewer orbits in the habitable zone, there are more planets. With just one planet per orbit we were able to fit 14, 7, and 3 orbits of planets of 0.1, 1 or 10 times Earth’s mass. Including co-orbitals we can only fit 9, 5 and 2 orbits. But two planets per orbit makes it 18, 10 and 4 planets in the habitable zone. Give them each a large moon and the numbers are doubled. Boom!
As we saw previously, a system of gas giant planets tends to have different orbital spacing (in resonances). The gravitational effects of Earth-sized Trojan planets don’t change anything in that case. So we could still fit four gas giant planets in the habitable zone of our chosen star. Of course, we can add in some ninja moves there too…
SUMMARY: Given one planet orbiting a star, stable islands exist on the same orbit: 60 degrees in front and 60 degrees behind the planet. A gas giant planet can have an Earth-sized planet in each of these points with no effect on orbital stability. Two (but not three) Earth-sized planets can share the same orbit, separated by 60 degrees. These are called co-orbital or Trojan planets. Wider orbital spacing is needed for a system of co-orbital planets.
OVERALL SUMMARY: We are becoming ninjas! With moons and co-orbitals, many worlds can share the same orbit. This means we can pack more Earth-sized worlds into the habitable zone.
Up next: putting the pieces together to build our ultimate Solar System.
Will co-orbital planets tend to stay about 60° from each other or will they play catch up like Janus & Epimetheus in the Saturn system
ISTR reading that the the trojan configurations gets unstable when the smallest of the 3 bodies gets a mass that is a significant fraction of the 2nd largest body. Is that correct?
Co-orbitals will indeed stay at about 60 degrees separation. There are other types of co-orbital configurations such as horseshoe orbits (like Janus and Epimetheus) or even eccentric 1:1 resonances that are extremely weird.
In terms of the mass ratios, the planets need to be less than about 1/30th of the stellar mass. This is no problem, since Jupiter is about 1/1000th of the mass of the Sun, so anything up to about 30 Jupiter masses can participate in a co-orbital configuration. The two planets can have the same mass.
I know I’m coming late to the party here but just in case you are still watching…
Are the L4/L5 points really stable enough long-term for a large planet? Isn’t it widely hypothesized that such a planet did indeed form as a co-orbital of Earth but ultimately became perturbed out of the stable point and struck the earth (creating the Earth-Moon system)?
Hello. I just discovered this site and I have a question. You wrote concerning the binary worlds: “This means that a day should be about a month in length.” Why is this so? My understanding of Pluto and Charon is that they orbit each other in a little over 6 days. I am enjoying much of what you have written and like the site.
To follow up on my comment above, let us say that instead of the Planet Mercury and the four Jovian moons, we had a world that was the size of these five placed together as one (such as hypothesized here: http://www.askamathematician.com/2011/01/q-can-we-build-a-planet/ ). Let us assume that the aforementioned new planet functioned as a large moon of Venus. If this were to be a binary pair, how long would the days be on this locked duo? I appreciate any time you devote to this.
Just a quick question about the binary planets: Do the sides of the planets facing each other get sunlight, or does it remain in darkness?
Well, the same sides of the planets always face each other, but they still spin with respect to the star. So, the length of the day on each planet is the time it takes the planets to orbit each other.
The problem here may be that the tidal effects of the star will also produce strong effects. I have to think this one through carefully, but perhaps all the planets, in all the locations, will also become tidally locked to the stars.
For a binary planet, at this point in time, I imagine double lock with respect to each other and the star. I am not yet sure what this would mean for orbital periods, stability or resonances between the other closely packed planets.
For that matter, when you require that the middle of the habitable zone be 0.1 AU from the star, the width of the habitable zone becomes on the order of ~ 0.05AU. If you want to fit 4 orbits into such a zone, and assuming perfectly circular orbits, at closest approaches the separation between planets in adjacent orbits would be about 6 times the average moon distance. You said that there is enough “dynamical space” around even small stars (i.e. middle of habitable zone at 0.1 AU) to fit 4 orbits containing gas giants… but I am not sure what a gas giant passing within 6 moon distances do to a binary Earth over time.
While all this is fun to imagine, I suspect the 16 star system and specifically the requirement to keep 4 gas giant orbits within the habitable zone, is pushing if not breaking the limits of stability and tidal locking.
Thanks.
Just another quick question: Would a binary planet have an axil tilt?
Because of strong tidal effects between the binary planets they would each likely have very low obliquities (axial tilts) relative to their mutual orbit. However depending on the orbital distance to the star (and hence the strength of tidal effects between the star and each planet) their mutual orbital plane would not have to be aligned with the plane of their orbit around the star.
In the systems you describe, with habitable zones as close as about 0.1 AU, star planet tides would be strong. Though, I am not sure what the effect of stellar tides on double planets is over time. Is it an alignment of the binary orbit to the stellar orbit?
Very good question! That is something that astronomers have only just started thinking about. It’s a tricky problem!
Thank you for the reply 🙂 Please post the journal articles when some answer become available.
Hey Sean, a question: In a system with a gas giant and four to five large moons, is it possible for the outer moons to resist becoming tidally locked?
Definitely. Tides get weaker the farther you are from the planet so you can definitely imagine outer moons having much weaker tidal coupling.
I’m loving this series, the star system you made is insane, so it lend me the courage to ask you if such system would be possible:
A low density gas giant is eventually set against the orbit of an ice giant due to the presence of a bigger object (say, a brown dwarf) near its orbit while their orbits were still being stabilized.
Instead of colliding with each other, due to their distance, they eventually simply find a balance, becoming binary gas giants. Due to their Roche limit being changed due to their barycenter, all moons are shattered. Their ring is wide enough to not be close enough to fall on them, so it keeps floating around both objects, like a moon would with a binary planet.
Is it possible? If it is, would the influence of both objects affect the core of the gas giant enough for it to become a puffy planet even though not particularly close to its star?
Either way, thank you for the awesome reads and for sharing the passion I have for double planets =)
Let me unpack this… So there is a binary gas giant (well, ice giant + bigger gaseous planet). I agree that this would probably make it difficult to have stable moons, unless the binary orbit was pretty wide and the moons pretty close to each planet. Like you say, it’s not clear there would be a stable region that was not within the Roche limit, although there could still be puny moons inside that limit.
Alternately, if the binary orbit was quite close you could imagine a moon orbiting outside the combined binary. That part is plausible.
The gas giant binary would evolve due to tidal interactions, and would get wider in time, by the same process as the Moon is receding from the Earth. There would be heat deposited within each planet that could possibly puff them up, but that is a tricky one. In time, the binary would become unstable when tides made the orbit too wide. That critical separation depends on the orbital radius around the star — binaries are much less stable closer-in.
Could you arrange six planets at 60° intervals in the same orbit around a star, and get a stable system? With each planet at the L4 point of the planet behind it in the orbit, and at the L5 point of the planet in front of it? Larry Niven wrote about a similar configuration, back in the 70s, but that was without a primary at the centre, and I’ve never been sure it would work.
Good question — I do not think that is stable. Celestial mechanics studies find that the minimum number of planets needed to create a stable ring is 7. See here for that setup: https://planetplanet.net/2017/05/03/the-ultimate-engineered-solar-system/
Outstanding. Thanks very much, Sean. (Sorry it took forever to realize you’d replied.)
You mentioned Janus-Epimetheus style co-orbits, or Horseshoe orbits as you called them. I find these fascintating and think you may be able to pack a lot of planets into a single orbit using them. But it’s possible they would be unstable.
Consider two planets in such an orbit, call them A0 and B0. They’re both in circular orbits about 1 AU from the sun, but A0 starts out some small distance (say about 20,000 Km) closer. They do the Horseshoe orbit-swap thing every so often. So this should be stable, although one may have to remove perturbing outer planets (i.e. Jupiter) to keep them that way.
Now add two more planets (A1 and B1) to the same orbit. A1 has the same orbital characteristics as A0, except it’s 180 degrees opposite in its orbit. Ditto for B1 and B0. So now A0 is doing the orbit-swap alternately with B0 and B1 and A1 is doing the same only with the other of the pair. We now have 4 inhabitable planets sharing essentially the same orbit.
Can we add more? Perhaps 4 more planets set up 90 degrees away in the same orbit. That would be 8 planets. And yet more? Planets 45 degrees away in that same orbit to bring the total to 16? At some point I’m sure the system will become unstable and I suspect it’ll be before we get to 16, possibly even before we get to 8.
I’m fascinated.
Let’s postulate a binary exoplanet about 30 light years away, with an aggregated mass of (let’s say) about 3 earth masses. Given our current abilities and methods to find exoplanets, would we be able to detect it as binary? Or would it rather be filed as super earth?
And – given an alien civilization at roughly the same technological level as we are – how nearby they would have to be to detect our earth-moon system as an almost-binary planet?
You could combine these “ninja moves” and make trojan moons or moons of moons to cram in even more habitable worlds.